Have you ever booked a ski holiday and on day one realised that the resort is just wrong? That it's packed with school kids, perhaps, or has crappy snow or no steep off-piste for you to exhibit your amazing prowess. But you've paid for that six-day lift pass and committed to your chalet: there is no escape, and by day three you're as fed up and jaded as a seasonnaire in April.

If only there was a resort that had it all: endless backcountry plus baby slopes; unspoilt villages and the swankiest hotels in the world; history, cool après ski and silent nights. A perfect resort for all. Does it exist? Probably not, but there is a ski holiday that provides so many variations of the basic elements that it's bound to please everyone. That holiday is the ski safari.

I'm not talking about bimbling around with binoculars spotting marmots. The idea is that you ski a different resort each day: so you start every morning with that first-day-on-the-slopes feeling. And because you stay in a few different places, you are actually travelling – seeing a bit of the world instead of retreating into a ski resort bubble.

The concept works best when there are marked differences between a cluster of resorts, yet where moving among them doesn't involve a Top Gear-style ice-driving challenge, or sitting for hours in a tunnel, thinking about the Mont Blanc fire.

America is a great destination for this, especially if someone else makes the arrangements. UK operator Ski Safari claims it pioneered the slope‑gypsy package a decade ago and now offers 13 self-drive itineraries in the US and Canada (plus five in Japan and Switzerland), including some creative new combinations, such as a two-centre trip to Whistler and Hawaii. The one I went for, to Utah, packs in a week's skiing in five or six resorts around Salt Lake City (the state has 14 resorts), then a road trip through several national parks, ending up in Vegas for what would possibly be the most extravagant après ski ever.

Accompanied by my ski-mad boyfriend on week one (to be swapped for a girl buddy, a Thelma, for week two), I went first to The Canyons, a purpose-built resort less than an hour's drive from the airport (if you discount the 10 minutes I spent in a Toys R Us car park panicking about having to drive the enormous 4x4 included in the package).

Few British skiers are familiar with The Canyons, but it is now one of the five biggest ski resorts in America, with nine mountains, 19 lifts, 167 trails and six hotels. Several other resorts are within an hour or so's drive.

My safari lodge for four nights was the Grand Summit, a 350-room sprawl of dark wood, open fires and chintzy restaurants that was doing a poor impersonation of a traditional wood cabin, channelling that soap opera-set phoniness common to most big, modern American hotels. But on the upside, there were outdoor hot tubs and it was so close to the slopes that transit from pancake-laden breakfast table to gondola was less than five minutes.

A pancake breakfast sets you up for the day's ski safari. Credit Required/PR

Utah has done something that could only happen in America, and that is to trademark the weather: its snow is officially The Greatest Snow on Earth™ (what next, gusts of wind sponsored by Nike?) on account of the 500 inches that fall there every year, and its unusual lightness and dryness.

No snow had fallen for days, but it wasn't hard to find still-fresh powder, so vast but uncrowded was the resort. Up the Ninety-Nine 90 lift to the resort's highest point (9,990ft), a backcountry access gate covered in signs telling skiers how not to die in an avalanche led to a ridge hike up above the clouds, and a wide expanse of deep powder on the west side of the mountain, descending steeply to a forest.

We played around in the gullies, natural half-pipes and chutes through the aspen and pines at the bottom, before seeking out more powdery steeps off the Peak 5 lift, refuelling in the outdoor grills and waffle stands that add a cutesy touch to this varied resort. Only the characterless base village was a letdown, with its weird empty plaza piping tinny pop music to nobody, and fast-food restaurants where chairs were on tables by 8.30pm.

On the second night, we booked a special Viking Yurt dinner in a cosy hut on the mountain, reached on a giant sleigh towed by a piste-basher. The place was billed by NBC's Today Show as "one of the most romantic places to propose in America", so we were a bit peeved to find strangers were grouped together on tables of six. A night spent discussing Joyce and Bill from Florida's triathlon training wasn't exactly what we had in mind.

The penny dropped eventually: even when staying at The Canyons, you need to spend the evenings at Park City, the 1860s mining town a four-mile shuttle-bus ride away. Park City's colourfully painted main street looks just like the ones in westerns, but with sushi bars and boutiques instead of brothels and gun shops.

It is the high street you need if you require a Native American feather headdress, some vintage wooden skis, toffee apples (one store sold nothing but), or a real-fur posing pouch.

It also has the most perfect poshed-up dive bars – every roadtripping Brit's dream. We longed to be regulars at O'Shucks – which had neon lights, surfboards, peanut-shell littered floors and quirky draught ales – or at the No Name Saloon & Grill, with its moose heads and fairy lights. There was even a ski-to-the-door whiskey distillery with bar, called High West, of which all other ski resorts must be jealous.

Park City has its own fun, family-friendly but gnarly-edged ski resort, with 107 runs, some of which take you past interesting abandoned silver mining buildings, which you can learn about on a guided history tour by skis.

Instead we hiked some short but brilliant off-piste tree runs in McConkey's Bowl and rode through the middle of a terrifying superpipe where Shaun White, Torah Bright and other pros practise. Then we relaxed and embraced the silly side of snow sports, riding a ridiculous toboggan-style rollercoaster and later, after several (locally distilled) courage-lending whiskey cocktails, attempted the floodlit jumps during the night skiing session.

Next safari stop: Deer Valley. In the same valley as Park City and The Canyons, but totally different; a sort of utopian snow-world for rich people, which aims to give skiers five‑star hotel service throughout the resort. That means lift stations resemble Michelin-starred restaurants, lift attendants act like butlers and equipment rental staff fawn like you're in a luxury spa. There was something sickening about the sheer upmarketness of it all, but being forced to revert to skiing for the first time in 15 years, I was giddy with the novelty of remembering how to snowplough and ended up loving the resort's safe, short and immaculately groomed runs, designer mountain coffee huts and cosseting atmosphere.

There was a totally different vibe in the parallel valley, the Big Cottonwood Canyon, home to Solitude and Brighton. On the way I accidentally drove the wrong way up a four-lane highway. It was definitely time for coffee. As if by magic, a dream of a roadside diner materialised in the form of the Silver Fork Lodge, where we learnt that pancakes with cream cheese, bacon, maple syrup, bananas and walnuts are a very good thing.

Solitude was a small, free-spirited resort with eight lifts, 64 runs, much less development and a lot of soul. Armed with a guide, Joe, who led us along tricky traverses into Honeycomb Canyon, we left the beginners' runs to discover what Solitude is really all about: steep, advanced terrain.

"All the boot hiking deters a lot of people," said Joe when we noted the lack of other skiers, "but we keep the snow better than all the other Utah resorts. We often have seven feet of snow when the others have five."

That night, as we relaxed in the hot outdoor pools of our wonderful lodge, the Inn At Solitude, the Greatest Snow On Earth™ pelted down.

In my boyfriend's ideal world, we would have headed to Alta, the extreme skiing mecca in Little Cottonwood Canyon, the next valley along, but as snowboarding is banned there we visited its neighbour, Snowbird, instead. As well as having the coolest logo of any resort, Snowbird had the steepest terrain we found: scary narrow lines through tightly packed trees off the blue Chips Run, and thrilling double-blacks such as Barry Barry Steep and Gad Chutes.

Once again, this was a completely different experience from the rest of the week. I would have liked to spend longer in every single resort, but I wouldn't have wanted to miss out any of them.

Finally it was time to shake things up even more, and I was waving goodbye to my bloke at Salt Lake City airport and picking up my Thelma. Heading south towards sunnier climes, I'd mentally put away all thoughts of snowboarding and relegated my salopettes to the bottom of my bag, when I suddenly spotted an opportunity not to be missed. The Coral Pink Sand Dunes state park, a sweeping expanse covering 3,730 acres, and just a small diversion off our route, had become popular for sandboarding, said the guidebook. I had my board – it felt rude not to stop by. The rosy undulations were empty and beautiful, but confusingly covered in snow, so I'm not sure which sport we were doing as we took turns to slide over the pink and white stripes.

The further we drove away from the ski resorts, the more Utah's true colours began to show. Thanks to the Mormon pioneers who settled there, Utah is 60% Mormon and one of America's most religiously homogenised states.

They are not shy about it. When the car's CD player malfunctioned at the start of our 300-mile drive and our carefully prepared road-trip soundtrack became redundant, we could only find two radio stations, both broadcasting nothing but Mormon sermons. When we finally collapsed on the beds of our Best Western lodge in the Bryce Canyon national park and rang up for a beer from room service, we were told, "Sorry ma'am, this is a dry state. Beer is only sold with food and you will have to go up the road to the Ruby's Inn restaurant."

Bryce, a tourist honeypot in summer, was empty when we trekked in the next day: the only sounds were the drip-drip of melting snow and the tinkle of falling rock shards. Snow made it even more magnificent, contrasting dramatically with the red of its spire-like hoodoo rock formations and the green of the pines.

Having felt an urgent need to photograph every inch of this magical, geologically unique wonderland, we set off on a snowshoe walk to the spectacular Pariah viewpoint a little later than planned. Eventually, though, we set off on our last activity of the day, cross-country skiing on a small circuit through the park's pretty ponderosa pine forest. Earlier that morning the jolly park ranger at the visitor centre had reassured us that, yes, you have plenty of time to do all three activities in one day. I guess he hadn't factored in the fact we had never cross-country skied before.

Thelma revealed she'd never even been ice-skating before. And cross-country skiing is harder than it looks. I couldn't get the rhythm. We spent a lot of time on our bums. But it was so fun! So beautiful! Especially when dusk fell and the stars began to twinkle. Only when it became properly dark did we realise we were in trouble. The path, which in the beginning had been carved wide and deep by dozens of ski tracks, diminished to two, then disappeared. It was too far to go back.

So many American films involve dumb-ass protagonists getting lost in the wilderness that when it happens to you, it's hard to work out if you are a victim of Hollywood-inspired paranoia or really are wandering mindlessly into a life-or-death situation.

I was convinced our route lay on the other side of a forested hill, but getting over it was impossible for someone who'd never skied before. We remembered passing a road about 15 minutes back, so headed off the path into the deep snow towards it.

It was pitch black and freezing when we reached tarmac. Now which way? We had no map, no phones, no light, so took a guess. But, nightmare of nightmares, we couldn't get our stupid cross-country ski boots to detach from our stupid skis. Exhausted, with bleeding, blistered feet and no path, we simply could not ski any further. And so we took off the skis, boots and all, and walked in our socks. In sub-zero temperatures. For hours.

We had no idea if we were even on the right road. Some led off for hundreds of miles into snowy wilderness. We started to freak out.

"There are no bears, there are no bears," I repeated to myself, glad (sorry) that grizzlies had been eradicated by hunting in the area. We argued about whether to sing, or if that would definitely mark us out as horror film fodder. We abandoned the stupid skis by the side of the road, arranged in the ominous X that indicates emergency. Eventually, several hours after we'd set off on our lovely cross-country jaunt, something hulky loomed ahead. I held out the car key and prayed, harder than those radio Mormons. Blipblip. It was one of the best moments of my life.

After that memorable debacle, we also had an interesting cultural experience as we drove through Arizona, en route to Zion national park. We saw on the map we were to pass Colorado City, infamously the centre of the fundamentalist branch of the Mormon church, the one that does the polygamy. There, powerful, ugly religious leaders "marry" several young, often underage wives, forcing them to breed relentlessly. Those that escape, and the dozens of teenage boys who are banished each year, often report child abuse and rape. Wrong as it may be, we decided to take a look. It was a ramshackle, poor and creepy little town. In the supermarket, serious-faced blonde girls, all wearing Little House on the Prairie style flowery smocks, with big quiffed hair, carried babies and stared at the strangers who had ignored the guidebook advice and come to town. It felt like the most foreign place I'd ever been. We didn't stick around.

Zion was full of stunning red rock canyons. We hiked in warm sunshine up a zig-zagging route called Walter's Wiggles, which led to the scariest path I have ever seen: Angel's Landing, a steep narrow strip with a sheer drop on each side. I didn't even try to tackle it. Instead we retreated to the galleries, cafes and boutiques of quirky Springdale, the town next to Zion.

And finally, Vegas. I got a few funny looks dragging my snowboard bag into the super stylish Vdara hotel, but what a way to end!

Safaris are supposed to be about spotting the Big Five. But totting up all the backcountry thrills, the scary hikes, the epic drives, the unexpected adventures, I calculate there must have been at least a Big 105 in that one great adventure. It might just have been The Greatest Holiday in the World™.